Distributed Nash Equilibrium Seeking for Aggregative Games with Quantization Constraints

The problem of seeking Nash equilibrium (NE) based on aggregative games under quantization constraints is full of challenges. Although the NE seeking algorithm in continuous-time systems has been studied, this problem in discrete-time systems still needs to be solved urgently. To address this problem, three distributed algorithms are first proposed under three quantization cases, adaptive, random, and time-varying quantizations, based on doubly stochastic communication topology networks. Then, the actions of players would eventually converge to NE under the conditions of vanishing step size and strong monotonicity are proved. Moreover, the convergence rate of the three quantization cases are analyzed, respectively. Finally, numerical experiments are implemented on plug-in hybrid electric vehicles (PHEVs) to validate the effectiveness of the proposed distributed algorithms. Comparing the convergence rates of the three proposed algorithms, the convergence effect of the adaptive quantization is better than that of the other two quantization cases.